Thermoeconomic diagnosis of complex energy systems is probably the most developed application of thermoeconomic analysis [NATO ASI on thermodynamics and optimization of complex energy systems, 1999, p. 117]. It is applied to diagnose the causes of the additional fuel consumption of a steadily operating plant, due to the inefficiencies of its components. In this paper, a new method based on the structural theory and symbolic thermoeconomics [Energy 19 (13) (1994) 365] is introduced. It integrates the thermoeconomic methodologies developed until now, such as fuel impact and technical exergy saving [Flowers 94, Florence World Energy Research Symposium, Florence, Italy, 1994, p. 149] and let us to compute the additional fuel consumption as the sum of both the irreversibilities and the malfunction costs of the plant components. Furthermore, it will be able to quantify the effect of a component malfunction in the other components of the plant. As result, new concepts are included in the diagnosis analysis: intrinsic malfunction, induced malfunction and dysfunction. The key of the proposed method is the construction of the malfunction/dysfunction table which contains, in a very compact form, the information related with the plant inefficiencies and their effects on each component and on the whole plant. This methodology is not only a theoretical advance but also it enhances the thermoeconomic diagnosis applications, based on performance tests or simulation models. Some of them are presented in this paper using a simple example. The application of the methodology is shown in the second part of the paper.